Topological quantum compilation of two-qubit gates
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910711890837504 |
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| author | Burke, Phillip C. Aravanis, Christos Aspman, Johannes Mareček, Jakub Vala, Jiří |
| author_facet | Burke, Phillip C. Aravanis, Christos Aspman, Johannes Mareček, Jakub Vala, Jiří |
| contents | We investigate the topological quantum compilation of two-qubit operations within a system of Fibonacci anyons. Our primary goal is to generate gates that are approximately leakage-free and equivalent to the controlled-NOT (CNOT) gate up to single-qubit operations. These gates belong to the local equivalence class [CNOT]. Additionally, we explore which local equivalence classes of two-qubit operations can be naturally generated by braiding Fibonacci anyons. We discovered that most of the generated classes are located near the edges of the Weyl chamber representation of two-qubit gates, specifically between the local equivalence classes of the identity [1] and [CNOT], and between those of the double-controlled-NOT [DCNOT] and [SWAP]. Furthermore, we found a numerically exact implementation of a local equivalent of the SWAP gate using a sequence of only nine elements from the Fibonacci braiding gate set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological quantum compilation of two-qubit gates Burke, Phillip C. Aravanis, Christos Aspman, Johannes Mareček, Jakub Vala, Jiří Quantum Physics We investigate the topological quantum compilation of two-qubit operations within a system of Fibonacci anyons. Our primary goal is to generate gates that are approximately leakage-free and equivalent to the controlled-NOT (CNOT) gate up to single-qubit operations. These gates belong to the local equivalence class [CNOT]. Additionally, we explore which local equivalence classes of two-qubit operations can be naturally generated by braiding Fibonacci anyons. We discovered that most of the generated classes are located near the edges of the Weyl chamber representation of two-qubit gates, specifically between the local equivalence classes of the identity [1] and [CNOT], and between those of the double-controlled-NOT [DCNOT] and [SWAP]. Furthermore, we found a numerically exact implementation of a local equivalent of the SWAP gate using a sequence of only nine elements from the Fibonacci braiding gate set. |
| title | Topological quantum compilation of two-qubit gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.07132 |